The last column in the truth table of the statement pattern $[p \rightarrow (q \wedge \sim p)] \vee [(p \vee \sim q) \wedge p]$ is

Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.

The correct logical equivalences from the following are:
$(I)$ $p \to (q \to r) \equiv (p \land q) \to r$
$(II)$ $(p \to q) \to r \equiv p \to (q \lor r)$
$(III)$ $(p \to q) \to r \equiv (p \to r) \land (\sim q \to r)$
$(IV)$ $p \to (q \to r) \equiv q \to (p \to r)$

The logical expression $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

For each of the following statements,determine whether an inclusive "Or" or exclusive "Or" is used. Give reasons for your answer.
The school is closed if it is a holiday or a Sunday.